Bayesian Inference for Dynamic Treatment Regimes: Mobility, Equity, and Efficiency in Student Tracking

Abstract

Policies in health, education, and economics often unfold sequentially and adapt to changing conditions. Such time-varying treatments pose problems for standard program evaluation methods because intermediate outcomes are simultaneously pre-treatment confounders and post-treatment outcomes. This paper extends the Bayesian perspective on causal inference and optimal treatment to these types of dynamic treatment regimes. The unifying idea remains ignorable treatment assignment, which now sequentially includes selection on intermediate outcomes. I present methods to estimate the causal effect of arbitrary regimes, recover the optimal regime, and characterize the set of feasible outcomes under different regimes. I demonstrate these methods through an application to optimal student tracking in ninth and tenth grade mathematics. The proposed estimands characterize outcomes, mobility, equity, and efficiency under different tracking regimes. For the sample considered, student mobility under the status-quo regime is significantly below the optimal rate and existing policies reinforce between student inequality. An easy to implement optimal dynamic tracking regime, which promotes more students to honors in tenth grade, increases average final achievement 0.07 standard deviations above the status quo while lowering inequality; there is no binding equity-efficiency tradeoff. The proposed methods provide a flexible and principled approach to causal inference for time-varying treatments and optimal treatment choice under uncertainty.

Keywords: Bayesian causal inference, dynamic treatment regimes, time-varying treatment, optimal treatment, student

JEL Classification: C40, C21